Abstract:

Let$M^{n}(n \geq 3)$be a complete non-compact submanifold immersed in a space with constant curvature$N^{n+m}(c)$with flat normal bundle. By using Bochner-Weitzenböck formula, Sobolev inequality, Moser iteration and Fatou lemma, we prove that every$L^{\beta}~p$-harmonic forms on$M$is trivial if$M^{n}$satisfies some geometic conditions, where$\beta\geq p\geq 2$.

Key words: Submanifold, $p$-harmonic form, Vanishing theorem